In a summation notation, we can alternate the sign of each term by multiplying the entire sum (or equally, each term) by negative one to the n, n being the term count.
My question is if there are similar methods to arbitrarily create other repeating patterns, like: - - + + or + - + - - , just as examples. Keeping in mind that the intention is to also keep the integrity of the terms being multiplied, i.e., their absolute value remains the same.
I am aesthetically opposed to solutions which hinge on number theory functions like floor or ceiling, but that may just be due to my own deficiency to integrate them with my algebra skills.